In the quest to discover the properties of planar semiconductors, two-dimensional molybdenum trioxide and dichalcogenides have recently attracted a large amount of interest. This family, which includes molybdenum trioxide (MoO3), disulphide (MoS2), diselenide (MoSe2) and ditelluride (MoTe2), possesses many unique properties that make its compounds appealing for a wide range of applications. These properties can be thickness dependent and may be manipulated via a large number of physical and chemical processes. In this Feature Article, a comprehensive review is delivered of the fundamental properties, synthesis techniques and applications of layered and planar MoO3, MoS2, MoSe2, and MoTe2 along with their future prospects.